The peril of proportions: robust niche indices for categorical data

Abstract

Indices of niche breadth and niche overlap for categorical data are typically expressed in terms of proportions of resources use. These are unit-sum constrained data; hence, direct application of standard general linear modelling methods to such indices can lead to spurious correlations and misleading inference. To overcome these limitations, we introduce a compositional data analysis (CoDA) approach and derive compositional expressions of niche breadth, niche overlap and specialization. Compositional data analysis is specifically devoted to the analysis of vectors of proportions (i.e. compositions) and represents the appropriate framework for the study of sets of data with unit-sum constraint as those typically used in the calculation of niche indices. We show that compositional indices exhibit suitable statistical properties that make them flexible and robust, allowing downstream application of the full toolbox of multivariate analysis techniques to these estimators, a possibility not available with classical indices. In addition, we find that when characterizing niche breadth, niche overlap and specialization in terms of vectors of proportions, these concepts are naturally integrated in a coherent unifying framework. When data are categorical, we recommend the use of compositional indices for the statistical analysis of specialization metrics, niche breadth and niche overlap. We believe that the unified framework emerging from our compositional approach to niche metrics will allow a more thorough understanding of specialization at multiple levels of biological organization and provide novel insights in complex phenomena such as invasions and niche shifts